Argue for or against the strengthening of the power of state governments in the Federalist equation.
In recent years there has been a trend by so-called small government Congressmembers to shunt more and more authority--and the responsibilities that come with it fiscally-- to the states. These are often, in effect, unfunded mandates. For example, the state took over much of the welfare system when the federal programs ended and block grants were given to the states to fund such programs. Except the block grants could easily be scaled back over time, or not increased to accommodate a growing population. So the federal government transferred power to the states, but did so in a way that was unsustainable, knowing that eventually such programs would be cut.
There has always been a balance between the rights of states and the rights of the government. I do not think local control is always the answer. Take education for an example. School curriculum has historically been controlled by local school boards, and often political and monetary kickbacks and other forms of corruption dominated. After the standards movement, education became more state-controlled. However each state still has its own widely different standards, and methods of funding schools are different. Has local control been the best thing for American children?
Although the Tea Party fanatics call for more control by the states, they tend to forget that this very situation existed at the time of the Articles of Confederation. Indeed, at the time the Constitution was written, there were numerous "anti-Federalists" who opposed its ratification on the basis of denial of certain powers to the states as well as the lack of a Bill of Rights. The Constitution is flexible enough as written, particularly with the 10th Amendment which reserves specific rights to the States. A strong central government is necessary for defense and uniform administration of the law. More power to the states would be a dangerous trend.
The first answer seems to be assuming that you are asking about the writing of the actual Constitution. I assumed, when I read the question, that you were talking about strengthening the state governments now.
I would argue that we should not strengthen the state governments in most ways. Specifically, I do not think that the state governments should have the power to set their own goals for things like welfare and environmental protection or for issues of fundamental rights such as abortion or (perhaps) capital punishment.
When we let states set their own goals for welfare, for example, the states tend to "race to the bottom." As long as different states can have different goals, they pretty much have to compete to offer the least so that A) people don't move to their states to get welfare and B) so that they have lower taxes.
When we let states have different rules on abortion, for example, we give different Americans different fundamental rights. It is not right for a woman to have less control over her body in one state than another -- we are all Americans. It is not right (to look at it the other way) for one state to allow the killing of unborn Americans. Whichever way you look at it, abortion affects someone's fundamental rights and should not be up to the states.
I am in favor of states choosing how to do things like giving welfare. But I am not in favor of them choosing the goals -- how much welfare to give or abortion to allow, for example.
I think that when assessing the federalist position, one has to take into account their fundamental fears. The issue of Shays' Rebellion and the general state of weakness in federal government helped to create a setting where there was a need for centralized action. The failure of the Articles of Confederation in being able to put down Shays' Rebellion effectively as well as addressing the issues that gave rise to it convinced the federalists that some stronger form of government was needed. When framers like Jay and Madison envision the Constitution, they do so with the idea that a centralized government can be a source of both freedom and control. This was a vision that was set in stark contrast to the form of government in the Articles, where there was state freedom and autonomy, but little in ways of authority and structure. In the end, the federalists drew strength from the idea that freedom and autonomy are only as good as the structure in which these elements can be maximized. The "preservation of the Union" could only be envisioned with a strong central government that could maintain it.